A study of boundary shear stress, flow resistance and momentum transfer in open channels with simple and compound trapezoidal cross sections

• Main Author: Yuen, K. W. H.
• Published: University of Birmingham 1989
• Subjects: 532
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.492540

The characteristics of fully developed turbulent flow in smooth open channels of simple trapezoidal cross-section have been examined experimentally in the range 0.5 < Fr < 3.5,1.9 x 104 < Re < 6.2 x 105 and 0.3 < 2b/H < 15.0. Subcritical flow in a compound trapezoidal channel has also been studied for relative depths between 0.05 < Dr 0.5. The effect of secondary flows and the interaction between the main channel and the flood plain flows have been shown to influence the boundary shear stress and velocity distributions significantly. For simple channels, the boundary shear stress distributions have been correlated with the geometry parameters 2b/H or Pb/Pw, and empirically derived equations are presented giving the percentage of the total shear force carried by the wall. Ancillary equations are also presented giving the correlation between the geometry parameters and the mean and maximum shear stresses. Attention is also focussed on the effect of the hydraulic parameters on flow resistance. A comparison is made between the data and traditional formulations for smooth pipes and rectangular channels. The Froude number effect is also examined and found to be important. For compound channels, the transfer of momentum between the main channel and the flood plain has been studied in detail. Boundary shear force results have been used to calculate the apparent shear forces on vertical, horizontal and inclined interfaces. An empirically derived equation relating the geometry parameters and the boundary shear force on the flood plain bed and walls is presented. In order to quantify the momentum transfer within the whole section, the Navier-Stokes equation for steady uniform flow is used, and an analytical solution to the depth averaged form of the equation compared with the experimental results. A comparison of the depth-averaged values of flow resistance with those values obtained from a one-dimensional formulation is also made, and distinct differences noted. Improvement may be made by using the resistance radius in place of the traditional hydraulic radius. Use is made of the apparent shear force results in assessing channel discharge calculation methods which are based on sub-dividing the flow area. Equations are presented giving the main channel discharge for both vertical and horizontal division planes. The methods for evaluating the critical depth in a compound channel are also reviewed and assessed against experimental data. The free overfall for simple trapezoidal channels has been studied and an analytical relationship obtained between the ratio of brink depth to critical depth and the channel bed slope. Experimental data confirm this relationship.